The company revealed that an 'engineering fault' caused the leak but said this has not been identified.
This is because the leak took place inside a sealed concrete- lined unit where liquid plutonium is evaporated to form a solid oxide for storage.
A spokesman for BNFL said that in the first few hours after the leak, plant managers decided they could deal with it on their own, within a few days.
But once they realised the amount of plutonium liquid involved in the incident, the managers decided that the clean-up would need approval from the Nuclear Installations Inspectorate.
The company said no radioactive material escaped after the leak on 8 September, but its workers cannot enter the unit until the NII gives its approval for the clean-up to go ahead.
BNFL is still finalising its recovery proposals and expects to submit these to inspectors within the next few days.
The company said the four- week shut down would not cost them any money because it would not affect the reprocessing contracts it held with customers.
'It will just be a case of catch up when we start again,' a spokeswoman said.
'There is fuel in the plant waiting to be reprocessed, but the business is already there. We have plenty of storage room.'